This reply has gotten a lot longer than I expected. I was just trying to
come up with all the reasonable answers to the accelerating objects weighed
in water and came up with over a dozen ways the question could be answered!
If you actually make it through the post, perhaps you could vote on your
favorite definitions.
Before defining weight, let's define g! Ultimately it must be determined
experimentally, but for a uniform, spherical earth approximation, g can be
calculated from theory.
Definition 1: g(1) = F/m = GM/R^2
This is a good clean definition and seems to be what many books state, but
it disagrees with what is stated later, that an object you drop falls
toward the earth at that accleration
Definition 2" g(2) = GM/R^2 - R (omega)^2
If my figures are correct, this amounts to a correction of about delta =
0.03 m/s^2. Small but significant. And I believe this is what is most
often assumed.
Now to weight. Consider the cases in the previous post: m = 100 kg, g =
10 m/s^2, density = 5,000 kg/m^3; case a) in vacuum, Case b) in water; Case
1) a = 0, Case 2) a = +5 m/s^2 and Case 3) a = -5 m/s
Definition 1: weight = force due to gravity
Using g(1)=10 all answers are W = mg(1) = 1000 N
Using g(2)=10 all answers are W = m (g(2) + delta) = 1003 N
Definition 2: weight = force of gravity - effects due to rotation of earth
Using g(1)=10 all answers are W = m (g(1)+delta) = 997 N
Using g(2)=10 all answers are W = mg(2) = 1000 N
Definition 3: weight = what a scale reads (and the "elevator" is attached
to the rotating earth)
Using g(1)=10 W(1a) = 997 N W(1b) = 0.8 x W(1a)
W(2a) = 1497 N W(2b) = 0.8 x W(2a)
W(2a) = 497 N W(3b) = 0.8 x W(3a)
Using g(2) = 10 add 3 N to W(1a), W(2a) & W(3a)
Defintion 4: weight = what a scale reads (and the accleeration is indeed
straight up and not rotating with the earth)
Add 3 N to all answers in Def 3
Definition 5: Same as Def 3 but ignoring "extraneous" forces like bouyancy
I'm getting tired of typing - you figure it out.
Definition 6: Same as Def 4 but ignoring "extraneous" forces like bouyancy
I'm getting tired ot typing - you figure it out.
** And none of these address the question of your weight on a
merry-go-round! **
My favorites are g = g(2) (since that seems to be how "g" is typically
defined experimentally); and D5 for weight (since it goes well with g(2)
and I personally feel that bouyant forces don't change the weight).